<h2>Problem 43</h2>
<div style="color:#666;font-size:80%;">09 May 2003</div><br />
<div class="problem_content">
<p>The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.</p>
<p>Let <i>d</i><img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" /> be the 1<img src="" style="display:none;" alt="^(" /><sup>st</sup><img src="" style="display:none;" alt=")" /> digit, <i>d</i><img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" /> be the 2<img src="" style="display:none;" alt="^(" /><sup>nd</sup><img src="" style="display:none;" alt=")" /> digit, and so on. In this way, we note the following:</p>
<ul>
<li><i>d</i><img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>3</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>4</sub><img src="" style="display:none;" alt=")" />=406 is divisible by 2</li>
<li><i>d</i><img src="" style="display:none;" alt="_(" /><sub>3</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>4</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>5</sub><img src="" style="display:none;" alt=")" />=063 is divisible by 3</li>
<li><i>d</i><img src="" style="display:none;" alt="_(" /><sub>4</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>5</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>6</sub><img src="" style="display:none;" alt=")" />=635 is divisible by 5</li>
<li><i>d</i><img src="" style="display:none;" alt="_(" /><sub>5</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>6</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>7</sub><img src="" style="display:none;" alt=")" />=357 is divisible by 7</li>
<li><i>d</i><img src="" style="display:none;" alt="_(" /><sub>6</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>7</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>8</sub><img src="" style="display:none;" alt=")" />=572 is divisible by 11</li>
<li><i>d</i><img src="" style="display:none;" alt="_(" /><sub>7</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>8</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>9</sub><img src="" style="display:none;" alt=")" />=728 is divisible by 13</li>
<li><i>d</i><img src="" style="display:none;" alt="_(" /><sub>8</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>9</sub><img src="" style="display:none;" alt=")" /><i>d</i><img src="" style="display:none;" alt="_(" /><sub>10</sub><img src="" style="display:none;" alt=")" />=289 is divisible by 17</li>
</ul>
<p>Find the sum of all 0 to 9 pandigital numbers with this property.</p>

</div><br />
